Unit 1 Benchmark and Test Review

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the average rate of change for a car's speed from 2 to 8 seconds?

Back

Subtract the speed at 2 seconds from the speed at 8 seconds and divide by the time interval (8 - 2 seconds).

Front

What is the factored form of the expression 49b² - 100?

Back

(7b - 10)(7b + 10) is the factored form of 49b² - 100.

Front

What is the domain of a polynomial function?

Back

The domain of a polynomial function is always (-∞, +∞).

Front

What does it mean if a zero has a multiplicity of 3?

Back

A zero with a multiplicity of 3 means that the graph touches the x-axis at that zero and turns around, indicating it does not cross the axis.

Front

How do you factor a difference of squares?

Back

A difference of squares can be factored using the formula a² - b² = (a - b)(a + b).

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable and determines the polynomial's end behavior and the maximum number of zeros.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial.

Front

What does it mean for a polynomial to have a zero at x = 2?

Back

If a polynomial has a zero at x = 2, it means that when x is substituted with 2, the polynomial evaluates to zero.